MATH 21 Lecture Notes - Lecture 12: Row Echelon Form, Elementary Matrix, Gaussian Elimination
Document Summary
Example: use gaussian elimination to get reduced echelon form. Definition: elementary matrix matrix from elementary row operations: exchange (cid:4666)(cid:2869) (cid:2870)(cid:4667, scaling (cid:4666)(cid:2871) (cid:4666) (cid:883)(cid:4667)(cid:2871)(cid:4667, elimination (cid:4666)(cid:2870) (cid:4666) (cid:884)(cid:4667)(cid:2872)+(cid:2870)(cid:4667) The inverse of is elementary matrix of the same type. Note that (cid:1865) (cid:1866) matrices (cid:4666)(cid:1827)+(cid:1828)(cid:4667) are row equivalent if there is a sequence (cid:4666)(cid:2869),(cid:2870), (cid:4667) Such that =, (cid:2870),(cid:2869) (cid:4672)(cid:883) (cid:884)(cid:884) (cid:885)(cid:4673) (cid:4666) (cid:884)(cid:4667)(cid:2869)+(cid:2870) (cid:882) (cid:883)(cid:4673) (cid:4672)(cid:883) (cid:884)(cid:882) (cid:883)(cid:4673) (cid:4672)(cid:883) (cid:882)(cid:882) (cid:883)(cid:4673) (cid:884) (cid:4672)(cid:883) [(cid:1827) invertible =(cid:1827)~= a product of elementary matrices]
